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<p>We prove that if a pair of Kähler classes is <i>J</i>-nef, the <i>J</i>-flow on a compact Kähler surface converges to a weak solution of the Monge-Ampère equation in the sense of currents. We also establish the same convergence behavior for the deformed Hermitian-Yang-Mills flow. The method is based on a property of a limit of viscosity subsolutions.</p>

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Weak limits of the J-flow and the deformed Hermitian-Yang-Mills flow on Kähler surfaces: boundary cases

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月12日

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  • Rei Murakami

摘要

We prove that if a pair of Kähler classes is J-nef, the J-flow on a compact Kähler surface converges to a weak solution of the Monge-Ampère equation in the sense of currents. We also establish the same convergence behavior for the deformed Hermitian-Yang-Mills flow. The method is based on a property of a limit of viscosity subsolutions.